Quantum chemistry calculation using a calculator such as an arithmetic device is known.
For example, Patent Document 1 discloses a quantum state estimation method for estimating the quantum state of an atom or a molecule at high speeds. To be specific, according to Patent Document 1, by a computer program, a control/arithmetic unit divides a space in or near a substance into a plurality of three-dimensional regions (cells), assigns a normal distribution function to each of the cells, and sets it as a basis function. Further, by performing discrete Fourier transform of the potential energy of atoms or molecules mapped to the space, and thereafter, moving data of the rear half of a discrete Fourier transform data sequence arranged in each basic reciprocal lattice direction to the front of data of the front half of the data sequence, discrete Fourier transform shift data is obtained. After that, a Hamiltonian matrix and an overlap integral matrix for solving a Schrödinger equation by a numerical variation method are calculated by merely substituting the basis function and the discrete Fourier transform shift data to an analytic expression. Then, by solving a secular equation from the Hamiltonian matrix and the overlap integral matrix to obtain unique energy, a wave function is calculated. As a result, various useful physical quantities are calculated.
Further, for example, Patent Document 2 is a related technique. Patent Document 2 discloses a parallel synthesis method for efficient electronic state calculation of a macromolecule. To be specific, according to Patent Document 2, a macromolecule is divided into segments with a length or more at which a localized molecular orbital (LMO) can be constructed and with the number of atoms or less that can be calculated by a well-known electronic state calculation method. Then, only an active LMO is extracted and, the atomic orbital of a terminal part away from an interaction part in the active LMO is removed and, by using the result as a calculation target, the electronic state of the entire macromolecule is solved as an eigenvalue problem based on a localized molecular orbital localized to a part strongly interacting with the coupling of the segments. Such a configuration can increase the efficiency of calculation.
Further, for example, Patent Document 3 is a related technique. Patent Document 3 discloses a method of, in order to apply a divide-and-conquer method to quantum chemistry calculation that needs global calculation, using the electron density (density matrix) of a fragmented molecular chain to find energy by many-body expansion
Further, for example, Patent Document 4 is a related technique. Patent Document 4 discloses a method of, in order to apply a divide-and-conquer method to quantum chemistry calculation that needs global calculation, using the electron density (density matrix) of a fragmented molecular chain and, in the calculation, building a buffer region in the surroundings to incorporate an effect of the environment.    Patent Document 1: Japanese Unexamined Patent Application Publication No. JP-A 2013-156796    Patent Document 2: Japanese Unexamined Patent Application Publication No. JP-A 2003-012567    Non-Patent Document 1: Chemical Physics Letters, issued on Nov. 12, 1999, vol. 313, pp. 701-706    Non-Patent Document 2: Physical Review Letters, issued on Mar. 18, 1991, vol. 66, pp. 1438-1441
In quantum chemistry, one of the calculation targets is an all-electron wave function. There has been a problem that as a molecular system that is a calculation target becomes large scale, finding an all-electron wave function requires very large order computational complexity and main memory usage. This is because, for example, calculation and storage of two-electron integrals are required in the calculation process, the number thereof is the order of the fourth power of the number of one-electron basis functions and, in the high-precision calculation, the number of multi-electron basis functions required according to approximation accuracy is on the order of 5 to 7 or more of the number of electrons and one-electron basis functions.
On the other hand, the technique according to Cited Document 1 is a technique for high-speed estimation of the quantum state of an atom and a molecule, and it cannot be applied to calculation of an all-electron wave function. Moreover, the technique according to Cited Document 2 enables calculation of electronic density and energy, but it does not enable an all-electron wave function.
Further, in order to calculate an all-electron wave function by using the techniques of Cited Documents 3 and 4, an extended method of Cited Documents 3 and 4 is used. In a case where such an extended method is used, it requires computational complexity and main memory usage of extraordinary order that is equivalent to the conventional method as a molecular system becomes large scale.
Thus, it has been difficult to solve a problem that it is difficult to suppress computational complexity in calculation of an all-electron wave function.